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GCE JUN 2008 : AS, F1: Further Pure Mathematics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2008 Mathematics assessing Module FP1: Further Pure Mathematics 1 AMF11 Assessment Unit F1 [AMF11] FRIDAY 20 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all six questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z AMFP1S8 3151 Answer all six questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 3 4 The matrix M is given by 2 1 (i) Show that the eigenvalues of M are 1 and 5 (ii) Find an eigenvector corresponding to the eigenvalue 1 2 [5] [3] (i) Construct the table for the symmetry group G of a non-square rectangle. Identify clearly any notation you use for the transformations. [7] The set {1, i, i, 1}, where i2 = 1, forms a group H under multiplication. (ii) Draw up the group table for H (iii) Show that the groups G and H are not isomorphic. 3 [4] [2] A system of equations is given by x + (1 a)y + z = 2 x + ay 2z = 6 ax + y z = 4 (i) Find the value of a for which this set of equations does not have a unique solution. [5] (ii) For a = 2, find the general solution. [6] AMFP1S8 3151 2 [Turn over 4 The circle C1 is given by x2 + y2 10x + 20 = 0 (i) Find the equation of the tangent to the circle C1 at the point (4, 2) The circle C2 is given by [6] x2 + y2 + 2x + 24y + 20 = 0 (ii) Show that the line found in (i) is also a tangent to circle C2 [5] (iii) (a) Find the point of contact of this tangent with the circle C2 [2] (b) Interpret this result geometrically. 5 [1] x 16 x 2 (a) The matrix P is given by 1 8 (i) Find the values of x for which the inverse exists. [3] (ii) Find the inverse of P, leaving your answer in terms of x [3] (b) The set of points which form the curve 2x2 + xy y2 x + 2y 3 = 0 1 1 2 is mapped by the matrix A = 1 0 Show that the curve formed by the image points has equation 4X 2 9Y 2 + 8X + 12 = 0 AMFP1S8 3151 3 [9] [Turn over 6 The complex numbers p and q are given by p = 3 4i q = 2 + bi where b is a real number. (i) If | p| = |q|, find the possible values of b [6] (ii) On an Argand diagram sketch the locus of |z p| = 6 [3] (iii) Using your diagram, or otherwise, find the minimum value of | z | for any point z on this locus. [5] THIS IS THE END OF THE QUESTION PAPER S 11/06 531-019-1 [Turn over

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Additional Info : Gce Mathematics June 2008 Assessment Unit F1 Module FP1 : Further Pure Mathematics 1
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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